Question: Solve for $x$ : $2x^2 + 4x - 48 = 0$
Solution: Dividing both sides by $2$ gives: $ x^2 + {2}x {-24} = 0 $ The coefficient on the $x$ term is $2$ and the constant term is $-24$ , so we need to find two numbers that add up to $2$ and multiply to $-24$ The two numbers $-4$ and $6$ satisfy both conditions: $ {-4} + {6} = {2} $ $ {-4} \times {6} = {-24} $ $(x {-4}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x + 6) = 0$ $x - 4 = 0$ or $x + 6 = 0$ Thus, $x = 4$ and $x = -6$ are the solutions.